Characterization of bending loss in hollow flexible ... · Characterization of bending loss in hollow flexible terahertz waveguides Pallavi Doradla,1,* Cecil S. Joseph,1 Jayant Kumar,2

Characterization of bending loss in hollow

flexible terahertz waveguides

Pallavi Doradla,1,*

Cecil S. Joseph,1 Jayant Kumar,

2

and Robert H. Giles1

1Sub-millimeter Wave Technology Laboratory, Department of Physics & Applied Physics, University of

Massachusetts Lowell, MA 01854, USA 2Center for Advanced Materials, Department of Physics & Applied Physics, University of Massachusetts Lowell,

MA 01854, USA *[email protected]

Abstract: Attenuation characteristics of hollow, flexible, metal and

metal/dielectric coated polycarbonate waveguides were investigated using

an optically pumped far infrared (FIR) laser at 215 µm. The bending loss of

silver coated polycarbonate waveguides were measured as a function of

various bending angles, bending radii, and bore diameters. Minimal

propagation losses of 1.77, 0.96 dB/m were achieved by coupling the

lowest loss TE11 mode into the silver or gold coated waveguide, and HE11

mode into the silver/polystyrene coated waveguides respectively. The

maximal bending loss was found to be less than 1 dB/m for waveguides of

2 to 4.1 mm bore diameters, with a 6.4 cm bend radius, and up to 150°

bending angle. The investigation shows the preservation of single laser

mode in smaller bore waveguides even at greater bending angles.

©2012 Optical Society of America

OCIS codes: (230.7370) Waveguides; (040.2235) Far infrared or terahertz; (110.6795)

Terahertz imaging.

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#169725 - $15.00 USD Received 4 Jun 2012; revised 16 Jul 2012; accepted 31 Jul 2012; published 6 Aug 2012(C) 2012 OSA 13 August 2012 / Vol. 20, No. 17 / OPTICS EXPRESS 19176

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1. Introduction

The Terahertz (THz) frequency regime of an electromagnetic spectrum is a rapidly

developing area in source and receiver technologies with a wide range of applications in

security screening and remote sensing [1]. The high sensitivity of THz radiation to water

concentration, resulting from the low energy interaction with the low frequency molecular

motions, has expanded its applications into the areas of imaging and spectroscopy [2]. Due to

its non-ionizing property (unlike X-rays), THz technology has become increasingly important

for biological applications. As cancerous tissues show higher hydration compared to the

healthy ones (Evident from PET and MRI studies) [3], the water detection by THz techniques

can be an alternative and easy way for cancer identification. The currently available

commercial THz imaging systems (TPI imaga 1000, et.al.) for cancer identification were

limited to the in vivo tissue analysis of externally growing tumors. A flexible cylindrical

waveguide with good mode selectivity is essential to guide the THz radiation in the field of

interior in vivo medical imaging. The functionality of the imaging system can be improved by

using low-loss, hollow, flexible terahertz waveguides with minimal transmission loss and

specific bending characteristics.

Terahertz waveguides have been fabricated from a variety of materials [4–6] and with

different cross sectional designs [7–10]. Practical hollow core THz waveguides with reduced

transmission losses below the level of 1 dB/m were reported recently [11–15]. Most of the

reported terahertz waveguides were either rigid or not quite flexible at larger bore diameters

greater than 5 mm [11]. On the other hand, the bendable terahertz waveguides were neither

cylindrical [7,10] nor provide low-loss (below 2 dB/m) [16,17]. However the flexible

cylindrical waveguides shown in the literature that provide low loss (1.3 dB/m) [12] do not

meet the small diameter requirement, as the fabrication technique is not feasible for bore

diameters less than 3 mm. Here we report the transmission and bending characteristics of low

loss (less than 2 dB/m), hollow, flexible, cylindrical terahertz waveguides with an inner

metal, and metal/dielectric coatings that are small enough in diameter for endoscopic

applications (2 mm bore diameter). These cylindrical hollow THz waveguides for medical

imaging were fabricated using flexible polycarbonate (PC) tubing, through an extrusion

process that provides a smooth inner surface. For this investigation silver (Ag) and gold (Au)

were chosen to be the germane metals, due to their high reflectivity values at 214.6 µm

wavelength. A dielectric layer is added to the flexible metal coated waveguides to improve

reflectivity within specific wavelength ranges. Polystyrene (PS) was chosen to be the

dielectric, due to its low extinction coefficient, that enhances the transmission through the

waveguide [18].


2. Experiment

Metal films were deposited inside the rigid or flexible tubes using an electro-less liquid phase

chemical deposition (ELPCD) process. The inner surface of the polycarbonate tubing was

coated with Ag using the ELPCD process in an open-loop configuration, whereas the

deposition of Au involved in a closed-loop [19] ELPCD process. Maximum transmission

through the THz waveguide can be achieved by depositing a metal film with a thickness

much greater than its skin depth at the desired wavelength. The duration of the deposition

process was about 2 to 4 minutes to obtain a several micron thick layer of Ag or Au, which is

much smaller than the time reported for a micron thick metal coatings in the literature. The

polystyrene coating was obtained by sending 5 to 8 ml of 16 to 20 wt% polystyrene/

cyclohexane solution through the metal coated waveguide with a maximum flow rate of 40

ml/min [20]. The thickness of the polymer coating increases linearly with time, and as

example, two SEM images taken at different coating times are shown in the insets of Fig. 1.

The desired 26.8 µm thick uniform PS film was achieved by coating the PC tube for 10

minutes using the closed-loop ELPCD process.

The source used for this experiment was a CO2 optically pumped far-infrared (FIR) gas

laser operating at 1.39 THz. The laser line used was 214.6 µm, horizontally polarized

transition in CH2F2, pumped by the 9R34 transition of the CO2 laser. Near the laser face, the

measured terahertz laser output power was 370 mW. The beam waist of the 1.4 THz laser was

measured as 2.36 mm. Maximal transmission in cylindrical THz waveguides can be achieved

by coupling the lowest loss TE11 mode into the metal coated waveguide and HE11 mode into

the metal/dielectric coated waveguides with maximum mode coupling efficiency. An optical

system was designed in such way that the ratio of the laser beam waist and bore radii, ω0/r, as

0.77, 0.64 mm to couple 90.3%, 98.1% of the lowest order TE11, HE11 mode into the metal,

and metal/dielectric coated hollow waveguides respectively [16,21].

Fig. 1. Schematic of experimental layout for the measurement of total loss in bent metal coated

waveguides. Insets show straight loss measurement and cross sectional SEM images of Ag/PS

waveguides at different PS coating times.

A 76.2-cm focal length TPX lens was used to collimate the THz beam. By using an 18-cm

focal length off-axis parabolic mirror (OAP), the collimated THz beam was focused into a 3.2

mm polycarbonate/glass tube (G) that cleans the higher order modes. A high-density

polyethylene lens was used to obtain the desired ω0/r ratio to couple TE11, HE11 mode into the

metal, metal/dielectric coated waveguides of various bore diameters respectively. A liquid

helium cooled silicon bolometer was used as the detector. The noise equivalent power (NEP)

of the detector was 1.13E–13 W/Hz1/2

and the system responsivity was 2.75E + 05 V/W. The

bolometer had a response time of 5 milliseconds with a gain of 200. An automated two axis

scan stage raster scanned the beam at both the ends of the waveguide to obtain the spatial

intensity variation. The resolution of both the horizontal and vertical axes was set to 0.01 mm.


The motion control and data acquisition software was programmed using National

instruments LabView®. A signal to noise (SNR) ratio of 68dB was achieved by using a lock-

in amplifier. The amplitude information from the silicon bolometer was sent to a Lock-In

amplifier and the data from the amplifier was collected by the program using a data

acquisition card from National Instruments. The software synchronized the motion control

and data acquisition, and generated an amplitude intensity map of the scanned area (≈1.5 cm

from the waveguide edge). The intensity amplitude sum is directly related to the power. The

power ratio of the input and output ends of the waveguide in Eq. (3) was obtained by taking

the corresponding ratio of the total intensity amplitudes, while maintaining the scanned area

(number of pixels) as constant in both the cases. The spatial profiles of the input laser beam

and output beam from the waveguide were verified by using a pyroelectric array detector

Spiricon Pyrocam III (≈1.5 cm away from the facet). Also, the total power values measured

exiting the waveguide for cutback loss measurements were verified using power meter with a

thermal sensor.

The set-up for measuring bending loss is shown in Fig. 1. The bending loss of the

waveguide depends on the bending angle, θ, and the bend radius, R. To facilitate the bending

radius measurement, an aluminum disc was used to bend the flexible waveguide as shown in

the experimental setup. R can be varied by changing the aluminum disc radius. In this

investigation three discs of different radii 4.2 cm, 5.1 cm, and 6.4 cm were used to bend the

silver coated waveguides of inner diameters 4.1 mm, 3.2 mm, and 2 mm up to 150°. The

power coupled into the waveguide was measured to be 3 mW.

3. Results and discussion

3.1 Propagation loss

The total transmission loss of a waveguide, αtot, is the sum of propagation and bending losses,

tot pq R

L L= + θα α α (1)

where αpq represents the propagation loss and αθ is the bending loss of the waveguide in

dB/m. L represents the length of the waveguide, and LR is the bend length.

The attenuation coefficient, αpq, for TEpq modes of hollow metal terahertz waveguides is

given by [16],

( )4 2

2 2 2 2 2 3 4

0

110

pq

u n pTE

u p n k r u r

= ⋅ +

− + α

κ (2)

where r represents the bore radius of the waveguide, ñ = n – iκ is the complex refractive

index of the metal, p is the mode index, k0 = 2π / λ0 is the wave number, and u is the phase

constant representing qth

zero of the Bessel function Jp’(x).

The straight losses for the hollow flexible 50 - 60 cm long silver, and gold coated THz

waveguides of different bore sizes were measured at 214.6 µm. The total transmission loss of

a waveguide was found experimentally using Beer-Lambert’s law as follows,

10

log in

out

P dBmL P

=

α (3)

where L represents the length of the waveguide, and P is the power. A cutback technique was

used to accurately determine the absorption coefficient for each straight waveguide. The loss

measurement for the entire length of the waveguide determines the value of Pout. The loss in

the residual short length waveguide that was left after the cut, determines the value of Pin. The

length of the waveguide is the difference between the long and short length of waveguide.

The attenuation coefficients were calculated with cutback method by using waveguides of six


different lengths from 10 to 60 cm. The transmission losses increase linearly with the

waveguide length. The linear fit to the data allows an estimation of total transmission loss and

experimental coupling efficiencies of the waveguide. The theoretical and experimental

attenuation coefficients in cylindrical metal coated waveguides were obtained from Eq. (2)

and (3) respectively. Figure 2 shows the theoretical and experimental attenuation coefficients

of both silver and gold coated waveguides as a function of bore diameter, d. The theoretical

and experimental results were found to be in good agreement. The experimental propagation

losses of the waveguides were generally higher than the theoretical losses. The predicted

trend of decreasing loss with increasing bore diameter, and the convergence of the attenuation

coefficient difference between silver and gold coated waveguides at larger bore diameters

were clearly visible from Fig. 2. The better agreement between experimental and theoretical

losses in case of gold coated waveguides can be due to the greater uniformity resulted from

closed loop ELPCD process. Propagation losses of 1.77 dB/m, and 2 dB/m were achieved

with 4 mm bore diameter Ag, Au coated terahertz waveguides respectively. Twelve tested 2 -

4.1 mm bore diameter silver, gold coated waveguides had experimental coupling efficiencies

between 74% and 79%.

Fig. 2. Experimental and theoretical attenuation coefficients as a function of bore diameter for

silver, gold, and silver/polystyrene coated terahertz waveguides.

Maximum transmission in metal/dielectric coated THz waveguides was achieved by

coupling the lowest loss HE11 mode. The theoretical attenuation coefficient for hollow

metal/dielectric coated THz waveguides is given by [22],

( )( )

222

2 2 23 20 0

110 1

2 1

d

pq

d

nu nHE

nn k r n

= ⋅ ⋅ + + − α

κ (4)

where n – iκ represents the complex refractive index of metal, u is the qth

zero of Jp-1(x). Here

ñd is the complex refractive index of the dielectric, which is assumed to be lossless. Both the

theoretical and experimental attenuation coefficients for silver/polystyrene coated 40 – 50 cm

long terahertz waveguides were plotted as a function of bore diameter d, as shown in Fig. 2.

The maximum measurement error for each individual data point calculated using the standard

deviations in the power measurement is less than 0.2 dB. The predicted trend of decreased

loss with increasing bore diameter, and the abatement in the difference of Ag, and Ag/PS

coated waveguides loss at larger bore diameters was clearly visible from Fig. 2. Also, the

Ag/PS coated waveguides show higher transmission compared to Ag coated waveguides for

all bore diameters. The discrepancy between theoretical and experimental attenuation

coefficients can be due to the edge coupling effect, roughness of metal or non-uniformity of

the dielectric coating. Also, the theoretical attenuation coefficients were calculated by

assuming a lossless dielectric (κd = 0). Due to the nonzero absorption coefficient of

polystyrene, with complex refractive index of 1.58 – i3.58x10−3

, the theoretical attenuation


coefficients in Fig. 2 should be at a higher level. In this investigation, the propagation loss of

less than 1 dB/m was achieved in 4 mm diameter silver/polystyrene coated terahertz

waveguides. Five out of the six tested 2 – 4.1 mm bore diameter Ag/PS coated waveguides

had experimental coupling efficiencies between 84% and 89%. The outlier has a coupling

efficiency of 77%, due to the non uniformity caused in 29.5 µm thick polystyrene coating.

Maximum coupling efficiency of 89% was achieved in 26.2 µm thick PS coated waveguide.

3.2 Bending loss

The bending loss in hollow flexible THz waveguides depends on the bend radius (R), angle of

bending (θ), and bore radius (r). In the mid-IR region it has been shown that, this additional

bending loss varies as r3/R [23]. The total loss for bent terahertz waveguides at 214.6 µm

wavelength is shown in Fig. 3. All the measurements were taken using 50 to 60 cm long

silver coated waveguides with the laser polarization perpendicular to the plane of bending (s-

pol). If the bending loss, αθ, is proportional to r3/R then,

( )3

3

tot pq R pq pq

rL L L C R L Cr

R

= + = + ⋅ = +

θα α α α θ α θ (5)

which means, if αtot is plotted as a function of θ at different bending radii for silver coated

waveguides of fixed bore diameter the slope must be constant. Figure 3(a) shows the total

attenuation coefficient, αtot, for a 3 mm bore diameter silver coated waveguide as a function

of bending angle, θ, at different bending radii 4.2 cm, 5.1 cm, 6.4 cm. It is observed that the

total loss increases rapidly with increasing bending angle or by decreasing bend radius. The

Y-intercept of Fig. 3(a) gives the straight loss, which is the total transmission loss, measured

when the bending angle was 0°. A bending loss of 0.8 dB/m was measured in 2 mm silver

coated waveguides with a bend radius of 6.4 cm. From Fig. 3(a), it is evident that the slope,

C, is invariant for the silver coated waveguides bent at different bending radii. As the slope of

the bending loss curve is independent of the bend radius, which confirms the result predicted

by Eq. (5) that, the bending attenuation coefficient αθ varies inversely with bend radius R.

Also, as the propagation loss, αpq, is proportional to 1/r3,

( ) ( )3

3 3 31

13 6/ / /

tot pq R

C r Lr L L r L C R r C C

Rr r

= + = + ⋅ = + θα α α θ θ (6)

Fig. 3. Total attenuation coefficient as a function of bending angle for the silver coated

waveguides of a) 3 mm inner diameter at various bending radii, b) different bore diameters

with 6.4 cm bend radius.

Figure 3(b) shows the total attenuation coefficient per r3, αtot/r

3, of the silver coated

waveguide with 6.4 cm bend radius as a function of bending angle for several bore diameter

tubes namely 2 mm, 3.2 mm, and 4.1 mm. It shows the direct dependence of total loss on

bending angle. Also it is observed that smaller bore diameters lead to a rapid increase in the


attenuation coefficient αtot/r3, as predicted by the presence of 1/r

6 term in Eq. (6). Further, the

maximal bending loss was determined to be less than 1 dB/m for all silver coated waveguides

with bore diameters greater than 1 mm. As the slope of bending loss curve in Fig. 3(b), C, is

invariant for the waveguides of different bore diameters, it is evident that the bending loss

varies as the cube of the bore radius as predicted from theory. The bending losses in 2 – 4.1

mm bore 40 cm long Ag/PS coated waveguides were measured up to 200 bending angle by

using an aluminum disc of 6.4 cm diameter. Due to the great difficulty involved in bending a

30 µm thick PS coated polycarbonate waveguide, bending losses are hard to measure at

greater bending angles without suppressing the uniformity of the PS layer. The maximum

bending loss measured in 2 – 4.1 mm bore diameter Ag/PS coated waveguides with 200

bending angle and 6.4 cm bend radius was 0.3 dB/m.

3.3 Modal characteristics

The output mode profile is most important for applications that require good beam quality and

preservation of Gaussian type modes. Modal characteristics of 50 cm long flexible silver

coated waveguides were obtained by using the experimental setup shown in Fig. 1. Spatial

intensity distributions of the propagated terahertz radiation through the silver coated

waveguides of different bore diameters, at various bending angles in linear scale were shown

in Fig. 4 and Fig. 5. The TE11 mode is dominant out of all the propagated modes in hollow

core metal coated waveguides, when excited with a linearly polarized THz wave, because of

the lowest attenuation constant among linear polarization modes. Hence an optical system

was designed to couple the TE11 mode efficiently into the metal coated waveguides. From the

input and output beam profiles of the 3.2 and 2 mm Ag coated waveguides with 0° bending

angle, it is evident that the launched TE11 mode fully developed at the output when

propagated through the silver coated waveguide. For the 4 mm diameter straight silver coated

waveguide we see that the output mode is not single mode but as the bore diameter decreases

to 2 mm the output converges to a single mode. This confirms the result shown by Harrington

et.al, when bore size is about 17λ the guide is multimode but when it is 12λ or less then the

waveguide becomes essentially single mode [8]. By maintaining ω0/r ratio as 0.77, we are

coupling only 90.3% of TE11 mode, there exist higher order modes in the waveguide. These

higher order modes attenuate rapidly in smaller bore waveguides as the loss is relatively

higher as shown in Fig. 4.

Fig. 4. The spatial intensity distribution of input for (a) 4-mm Ag, (b) 3-mm Ag, (c) 2-mm Ag,

(d) 3-mm Ag/PS and the output from (e) 4-mm Ag, (f) 3-mm Ag, (g) 2-mm Ag, and (h) 3-mm

Ag/PS coated straight terahertz waveguides.

In principle, metal waveguides do not preserve a single mode launched into the waveguide

while bending. The existence of higher order modes were observed in the output beam

profiles of 4mm diameter waveguide as it was bent. Even at greater bending angles, as


compared to 4 mm waveguide, guides with 3 mm bore diameter showed less mode mixing.

The smallest bore waveguides exhibit the least amount of mode mixing, as would be

predicted bythe general dependence of αpq on the mode parameter u in Eq. (2). That is, the

loss for higher order modes is relatively greater in small bore waveguides compared to large

bore sizes. This effect can be seen qualitatively in the mode profile data in Fig. 5 for three

different bore diameters of 4.1 mm, 3.2 mm and 2 mm.

The 2 mm diameter waveguide remains largely single mode even when bent to a radius of

6.4 cm, whereas the 3 mm diameter guide preserves the mode up to 50° of bending. But the 4

mm diameter waveguide shows a distinctly multimode pattern even when straight, and

bending further mixes the modes. The dramatic difference in modal properties between the

two sizes is largely due to their relative bore diameter sizes compared to the incident

wavelength. It was observed that the mode mixing was not severe in hollow glass

waveguides, as compared to PC waveguides at 0° bending angle, due to their inherent smooth

surface. Hence the discrepancy in modal properties may be due to the scattering from surface

roughness, which leads to coupling of energy into the higher order modes. When the metal

Fig. 5. Spatial profile of output from Ag coated waveguides of bore diameters (a) 4-mm, θ =

60°, (b) 3-mm, θ = 60°, (c) 2-mm, θ = 60°, (d) 4-mm, θ = 120°, (e) 3-mm, θ = 120°, and (f) 2-

mm, θ = 120° with 6.4 cm bending radius.

coated waveguides were loaded with a dielectric film, attenuation of TM modes will be

lowered, as a result HE11 mode becomes dominant out of all the propagated TE0n, TM0n,

HEmn, and EHmn modes [20]. It has been observed that the horizontal polarization of the

source beam is largely maintained in the Ag/PS coated waveguides, by inserting the

horizontal and vertical grid polarizers between the output end of the waveguide and the

detector. The mode profile of the straight silver/polystyrene coated waveguide of 3 mm bore

diameter shown in Fig. 4(d) and 4(h) is made up almost entirely horizontally polarized

radiation, and the intensity profile is the characteristic of the launched HE11 mode which

confirms the preservation of the single mode. That is, even when the bore size is about 15λ

the output mode was distinctively single mode. There is no significant change in the bending

loss and modal profiles of 3.2, 2 mm bore Ag/PS coated waveguides with 20° bending angle.

When the 4.1 mm waveguide was bent to 20°, due to the deformation of the circumferential

geometry can be caused in bending a larger bore diameter waveguide, some of the HE11 mode

energy is coupled into higher-order modes.

4. Conclusion

In conclusion, the propagation losses of Ag, Au, and Ag/PS coated waveguides of several

bore diameters were investigated at 214.6 µm wavelength. Total losses as low as 1.77 dB/m

and 2 dB/m were achieved in 4 mm Ag, Au coated waveguides respectively by coupling the

TE11 mode. The propagating modes transitioned from TE11 dominant to HE11 dominant as the


film thickness increased from 0 to 26.8 µm. Propagation losses as low as 0.96 dB/m were

achieved in a 4 mm metal/dielectric coated waveguide with 26 µm PS film thickness. Straight

Ag/PS coated terahertz waveguides of bore sizes up to 15λ showed the preservation of single

laser mode. The bending loss of silver coated waveguides for several bore diameters were

characterized as a function of bending angle, and bend radii. The total loss in a bent

waveguide increases rapidly with increasing bending angle or decreasing bend radius. The

maximum bending loss was determined to be as low as 0.8 dB/m for bore diameters greater

than 1 mm. Even when the bending radius was reduced from 6.4 cm to 4.2 cm, the increment

in the bending loss was found to be less than 2 dB/m. It was observed that the bending loss

varies proportionally to the cube of the bore diameter and inversely with bending radius. At

larger bending angles, output beam profiles of 4 mm bore waveguides showed higher mode

mixing, whereas the smallest bore 2 mm waveguides exhibited the least amount of mode

mixing. Our investigation indicates that the small-bore silver, silver/polystyrene coated

flexible waveguides preserves the single laser mode in addition to possessing a low bending

loss. The development of these waveguides can lead to increased applications in THz sensing,

communication and biomedical imaging applications.


Documents

Characterization of bending loss in hollow flexible ... · Characterization of bending loss in hollow flexible terahertz waveguides Pallavi Doradla,1,* Cecil S. Joseph,1 Jayant Kumar,2